Solution: COGO Intersections and Curves

Problem (1)

Part a.

Length and bearing of the straight sides and arc chord traveling clockwise travel direction around the parcel.

Compute coordinates of all the points using intersections. In the process, lengths and directions of some sides will be determined. Inverse between coordinates for those that aren't.

(1) Compute coordinates of point Q

(2) Using QB as a baseline, compute coordinates of T

Solve angle at T using Law of Sines:


Because angle T is greater than 90°,


Angle at Q:


Solve for LBT using the Law of Sines


Bearing BT:


Coordinates of T from B:

(3) Using QB as a baseline, compute coordinates of W

Solve angle at B using Law of Cosines:

Bearing BW:

Coordinates of W from B:


Math check - compute coordinates of W from Q (left to the reader).

(4) Using BW as a baseline, compute coordinates of K

Compute the angle at B:


Compute angle K from Law of Sines:

Since K is less than 90°, it does not have to be subtracted from 180°.

Compute angle at W from angle condition


Determine bearing W to K:


Compute coordinates of K from W

(5) Using coordinates, compute length and direction of Q to K

(6) Using coordinates, compute chord T to Q length and direction

Part b.

Central angle of curved side.

Line TQ is the arc chord - re-arrange the chord equation to solve the central angle

Part c.

Parcel area to nearest 10 sq ft

Using coordinate method, compute area bounded by straight lines. To that, add the segment area a for curve TQ.

(1) Area by coordinates

(2) Segment area

Total area = A₁ + A_seg = 60,371+3074.5=63,445.5 = 63,450 sq ft